Warne is desperate in his bid to bring a centre-half into his squad as he only has Clark Robertson, who has been playing left-back, Richard Wood and Michael Ihiekwe.
He met a target last week, who would come on a free transfer, and was pleased with how it went.
“The meeting went really well,” the boss said. "I'll speak to his club about Tuesday time, I reckon, and see.
“I would expect him to come in. Why wouldn't you want to come here, with all due respect? I do want him. He was a perfect character when we met him.
"Our dressing room is made of good characters. That's what I want.
"I explained to him how we treat people, how we try to better people, how we train, how we coach. I said, 'Go away, do your due diligence on us and if anything I've told you is a lie don't sign'."
Warne expects the player, whose identity has been kept under wraps but is from a higher league, still to come, even though he was told he would start off as fourth-choice.
Warne has been impressed with Robertson, Wood and Ihiekwe and has laid down a challenge to his potential new recruit.
He added: “I looked him in the eye and told him as honestly as I could, 'I love my centre-halves so you'd be coming here as fourth choice and you might stay fourth choice all season'.
"If that's the case, the other three will have done a good job."
After his side's League One game against Bury on Tuesday was postponed, Warne hit the road to meet another target, this time a winger.
"I'm definitely going to meet a wide man with a Championship club next week,” he said,
"We need to reinforce. We're constantly on it. I'm driving south and see a player and try to sell him the dream. The player would hopefully improve us but I've got to convince him there's a reason to come.
"We definitely need a wide outlet. We were screaming out for one against Burton. But we've won our two league away games playing three up front so that system is not too bad.
"With any luck, we should be able to buy a wide player, loan a wide player and get a centre-half in."